**Puzzle:**

At McDonald’s you can order Chicken McNuggets in boxes of 6,9, and 20. What is the largest number of nuggets that you cannot order using any combination of the above?

**Puzzle Solution:**

43

It is possible to achieve all multiples of 3 that are bigger than 6, through the 6s and 9s alone. Adding 6 to 6 will give you 12, and adding 6 to 9 will give 15, and you can obtain all subsequent multiples of 3 by adding sixes to one of 12 or 15.

And all numbers that are 1 less than a multiple of 3, that are 26 or higher (26, 29, 32, 35, 38, 41 etc) are 20 plus a multiple of 3, and as we previously said a multiple of 3 that is bigger than 6 can be achieved.

And all numbers that are 1 more than a multiple of 3, that are 46 or higher (46, 49, 52, 55, 58, 61 etc) are 40 (two lots of 20) plus a multiple of 3, and as before all multiples of 3 that are bigger than 6 can be achieved.

And since all (whole) numbers are either a multiple of 3, one more than a multiple of 3, or one less than a multiple of three, that covers all numbers above 43.